The editing
of the Babylonian Talmud took several centuries. The traditional
view credits the final editing to Ravina II (ca. 500) and is based
on the letter reproduced here, written by Sherira ben Øanina
(906-1006), the gaon of the rabbinic academy at Pumbedita in Babylonia.
Even he acknowledges, however, that the Babylonian Talmud was
not fully completed until the time of R. Yose more than a century
later.

.

Rav Ashi functioned as head of his academy for almost sixty
years. . . .

For this is what the rabbis instituted: to study two tractates
every year, whether long or short. So he [Rav Ashi] reviewed
his entire talmudic knowledge in thirty years. Since Rav
Ashi ruled close to sixty years, there were two cycles.
And he died in the year 738.